Repdigits as sums of three Pell numbers

In this paper, all base 10 repdigits expressible as sums of three Pell numbers are found.     

Organosulfonate Counteranions—A Trapped Coordination Polymer as a High-Output Triboelectric Nanogenerator Material for Self-Powered Anticorrosion

Selection of the friction electrode materials is crucial to the performance of a triboelectric nanogenerator (TENG). In the present study, a metal–organic coordination complex containing organosulfonate counteranions with electron-donating ability was synthesized through the coordination-driven self-assembly approach under mild reaction conditions and was chosen as a positive electrode material to construct a triboelectric nanogenerator, exhibiting high-output performance with a peak value of short circuit current density of 98.6 μA and an output voltage of 1180 V. As a practical application, it was shown to light up 1488 commercial green LEDs and power an anticorrosion system device to protect metals from corrosion.     

Bromine-Functionalized Covalent Organic Frameworks for Efficient Triboelectric Nanogenerator

Covalent organic frameworks (COFs) enable precise integration of various organic building blocks into porous skeletons through topology predesign. Here, we report the first example of COFs by integrating electron withdrawing bromine group onto the skeletons for triboelectric nanogenerators (TENG). The resulting framework exhibits high surface area and good crystallinity. Thus, the bromine functionalized COF has more regular aligned π columns and arrays over the skeleton than bare COFs, which in turn significantly enhances charge transport ability. As a result, bromine functionalized COFs showed higher electrical output performance at 5 Hz with a peak value of short circuit current density of 43.6 μA and output voltage of 416 V, which is 2 and 1.3 times higher than those of bare COFs (21.6 μA and 318 V), respectively. These results demonstrated that this strategy for engineering electron withdrawing groups on the skeleton could open a new aspect of COFs for developing TENG devices.     

Spatiotemporal Studies of the One-Dimensional Coordination Polymer [Fe(ebtz)2(C2H5CN)2](BF4)2: Tug of War between the Nitrile Reorientation Versus Crystal Lattice as a Tool for Tuning the Spin Crossover Properties**

Reaction of 1,2-di(tetrazol-2-yl)ethane (ebtz) with Fe(BF₄)₂⋅6 H₂O in different nitriles yields one-dimensional coordination polymers [Fe(ebtz)₂(RCN)₂](BF₄)₂⋅nRCN (n=2 for R=CH₃ ( 1 ) and n=0 for R=C₂H₅ ( 2 ) C₃H₇ ( 3 ), C₃H₅ ( 4 ), CH₂Cl ( 5 )) exhibiting spin crossover (SCO). SCO in 1 and 3 – 5 is complete and occurs above 160 K. In 2 , it is shifted to lower temperatures and is accompanied by wide hysteresis (T_1/2^↓=78 K, T_1/2^↑=123 K) and proceeds extremely slowly. Isothermal (80 K) time-resolved single-crystal X-ray diffraction studies revealed a complex nature for the HS→LS transition in 2 . An initial, slow stage is associated with shrinkage of polymeric chains and with reduction of volume at 77 % (in relation to the difference between cell volumes V_HS−V_LS) whereas only 16 % of iron(II) ions change spin state. In the second stage, an abrupt SCO occurs, associated with breathing of the crystal lattice along the direction of the Fe–nitrile bonds, while the nitriles reorient. HS→LS switching triggered by light (808 nm) reveals the coupling of spin state and nitrile orientation. The importance of this coupling was confirmed by studies of [Fe(ebtz)₂(C₂H₅CN/C₃H₇CN)₂](BF₄)₂ mixed crystals ( 2 a , 2 b ), showing a shift of T_1/2 to higher values and narrowing of the hysteresis loop concomitant with an increase of the fraction of butyronitrile. This increase reduces the capability of nitrile molecules to reorient. Density functional theory (DFT) studies of models of 1 – 5 suggest a particular possibility of 2 to adopt a low (140–145°) value of its Fe-N-C(propionitrile) angle.     

A cell-permeable green fluorescent probe for dsDNA

The sensitive and selective detection of nucleic acids is important for basic research and many applied fields. Herein, a novel green DEAB-TO-1 was designed and synthesized. DEAB-TO-1 shows significant fluorescence enhancement (800-fold) when bound to ctDNA and a distinct selectivity for dsDNA over RNA (5.9 times). Moreover, the limit of detection is 0.57 ng/mL. It is live-cell-permeant DNA intecalator, indicating a promising candidate for nucleus-specific imaging and a good counter-stain compatibility with other dyes.     

Usage of deep eutectic solvents for the digestion and ultrasound-assisted liquid phase microextraction of copper in liver samples

In this study, we used deep eutectic solvents for digestion and ultrasound-assisted emulsification liquid phase microextraction (UA-ELPME) of copper in liver samples. Different types of DESs were prepared for digestion and microextraction steps. DESs consisting of lactic acid and choline chloride for the digestion step and DESs consisting of tetrabuthylamonium chloride and decanoic acid for ultrasound-assisted emulsification liquid phase microextraction were used in this method. The liver samples were digested by using DES-based digestion method. After digestion step, Cu(II) ions in aqueous phase were complexed with sodium dimethyl dithiocarbamate (NaDMDTC) and the obtained hydrophobic complex was extracted to tetrabuthylamonium chloride-decanoic acid DES phase. A microsample injection system coupled with flame atomic absorption spectrometer (MS-FAAS) was used in the detection of copper. LOD, LOQ, PF and % RSD were determined as 4.00, 13.2 µg L^??1, 10 and 3.2%, respectively. The proposed microextraction procedure was successfully applied to copper contents of the liver samples.     

Isolated resonances and nonlinear damping

We analyze isolated resonance curves (IRCs) in single-degree-of-freedom systems possessing nonlinear damping. Through the combination of singularity theory and the averaging method, the onset and merging of IRCs, which coincide to isola and simple bifurcation singularities, respectively, can be analytically predicted. Numerical simulations confirm the accuracy of the analytical developments. Another important finding of this paper is that we unveil a geometrical connection between the topology of the damping force and IRCs. Specifically, we demonstrate that extremas and zeros of the damping force correspond to the appearance and merging of IRCs. Considering a damping force possessing several minima and maxima confirms the general validity of the analytical result. It also evidences a very complex scenario for which different IRCs are created, co-exist and then merge together to form a super IRC which eventually merges with the main resonance peak.     

Reflections on and of minor-closed classes of multisorted operations

The minor relation of functions is generalized to multisorted functions. Pippenger’s Galois theory for minor-closed sets of functions is extended to multisorted functions and multisorted relation pairs. Reflections of minor-closed sets are again minor-closed, and the effect of reflections on the invariant relation pairs of minor-closed sets of multisorted functions is described.